Shape optimization in contact problems. Approximation and numerical realization
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J. Haslinger, P. Neittaanmäki (1987)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Jaroslav Haslinger, Pekka Neittaanmäki, Timo Tiihonen (1986)
Aplikace matematiky
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.
Ivan Hlaváček (1987)
Aplikace matematiky
Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant...
Vladislav Pištora (1990)
Aplikace matematiky
The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences...
Ivan Hlaváček (1986)
Aplikace matematiky
A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
J. Pousin (2009)
Mathematical Modelling of Natural Phenomena
In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.
Miroslav Vondrák (1985)
Aplikace matematiky
The fundamental problem in the application of the principle of complementary energy is the construction of suitable subsets that approximate the set of all statically admissible fields satisfying both the conditions of equilibrium inside the body and the static boundary conditions. The notion “slab analogy” is motivated and the interface conditions for the Airy stress function are established at the contact of two domains. Some spaces of types of conforming equilibrium stress elements, which can...
J.-C. Paumier (1978)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
C. Johnson, B. Mercier (1978)
Numerische Mathematik
Frédéric Feyel (2002)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.
Frédéric Feyel (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.
P. Lascaux, P. Lesaint (1975)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Ben Belgacem, Faker, Brenner, Susanne C. (2001)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Jitka Křížková (1990)
Commentationes Mathematicae Universitatis Carolinae
Jitka Křížková (1991)
Applications of Mathematics
Special exact curved finite elements useful for solving contact problems of the second order in domains boundaries of which consist of a finite number of circular ares and a finite number of line segments are introduced and the interpolation estimates are proved.
Klaus Jürgen Bathe, Franco Brezzi (2001)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
We consider the formulation of contact problems using a Lagrange multiplier to enforce the contact no-penetration constraint. The finite element discretization of the formulation must satisfy stability conditions which include an inf-sup condition. To identify which finite element interpolations in the contact constraint lead to stable (and optimal) numerical solutions we focus on the finite element discretization and solution of a «simple» model problem. While a simple problem to avoid the need...
Pavel Bělík, Mitchell Luskin (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Pavel Belik, Mitchell Luskin (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to...
Wenhui, Mo (2010)
Mathematical Problems in Engineering
Saleh, M.M., El-Kalla, I.L., Ehab, M.M. (2007)
Differential Equations & Nonlinear Mechanics
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